Applied and Computational Mathematics (ACM)

Index Analysis

DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.

Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.

Group members working on that field

  • Andreas Bartel
  • Michael Günther

 

Cooperations

  • Giuseppe Ali (Academia)
  • Sascha Baumanns (Academia)
  • Caren Tischendorf (Academia)

Publications



1990

312.

Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990

311.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990

310.

Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990

309.

Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990

308.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

307.

Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H2F+ molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990

306.

Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990

305.

Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990

304.

Tausch, Michael W.; Kühn, S.
''Chemische Gleichgewichte - Elektrochemie'' - Diskette mit Programmen zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990

303.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2
Molecular Physics, 70 (3) :443-454
1990

302.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

301.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990

300.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse), 325 Seiten
Herausgeber: C. C. Buchner, Bamberg
1990

299.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

298.

Heilmann, Margareta; Müller, Manfred
Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators
Algorithms for approximation II, Proc. 2nd Int. Conf., Shrivenham/UK 1988, Seite 107-116
1990

297.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

296.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

295.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a1Δg → X3Σg-, b1Σg+ → X3Σg- and X1Σg+ → a1Δg systems of O2, SO, S2 and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

294.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

293.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

292.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0+ emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

291.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990

290.

Ehrhardt, M
Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990

289.

Ehrhardt, M
Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990
1989

288.

[german] Tausch, Michael W.; Wöhrle, D.
Photokatalyse
Praxis der Naturwissenschaften (Chemie), 38 :37
1989

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